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He took a few pupils, but not enough to hurt either himself or
his work. Making the best possible use of his liberty he con-
tinued the mathematical researches which he had begun as an
undergraduate. Like Abel, Galois, and many others who have
risen high in mathematics, Cayley went to the masters for his
inspiration. His first work, published in 1841 when he was an
undergraduate of twenty, grew out of his study of Lagrange
and Laplace.
With nothing to do but what he wanted to do after taking
his degree Cayley published eight papers the first year, four the
seconds and thirteen the third. These early papers by the young
man who was not yet twenty-five when the last of them
appeared map out much of the work that is to occupy him for
the next fifty years. Already he has begun the study of geo-
metry of n dimensions (which he originated), the theory of
invariants, the enumerative geometry of plane curves, and his
distinctive contributions to the theory of elliptic functions.
During this extremely fruitful period he was no mere grind.
In 1843, when he was twenty-two, and occasionally thereafter
till he left Cambridge at the age of twenty-five, he escaped to
the Continent for delightful vacations of tramping, mountain-
eering, and water-colour sketching. Although he was slight and
frail in appearance he was tough and wiry, and often after a
Jong night spent in tramping over hilly country, would turn up
as fresh as the dew for breakfast and ready to put in a few hours
at his mathematics. During his first trip he visited Switzerland
and did a lot of mountaineering. Thus began another lifelong
passion. His description of the 'extent of modern mathematics*
is no mere academic exercise by a professor who had never
climbed a mountain or rambled lovingly over a tract of beau-
tiful country, but the accurate simile of a man who had known
nature intimately at first hand.
During the last four months of his first vacation abroad he
became acquainted with northern Italy. There began two
further interests which were to solace him for the rest of his
Jife: an understanding appreciation of architecture and a love
of good painting. He himself delighted in water-colours, in
showed marked talent* With his love of good litera-